game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed ...

, perfect recall is a property of players within

extensive-form game In game theory, an extensive-form game is a specification of a game allowing for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfec ...

s, introduced by Harold W. Kuhn in 1953. it describes a player's ability to remember their past actions and the information they possessed at previous decision points. For example, in a simplified card game where a player makes multiple betting rounds, perfect recall means they remember their own previous bets and the cards they've seen. Essentially, it indicates that a player does not "forget" relevant information acquired during the game. It is important to distinguish perfect recall from

perfect information Perfect information is a concept in game theory and economics that describes a situation where all players in a game or all participants in a market have knowledge of all relevant information in the system. This is different than complete informat ...

. While perfect information means all players know all previous actions of all players, perfect recall means a player remembers their own past actions and knowledge.

Significance

Perfect recall is crucial for the consistency of rational decision-making in

sequential game In game theory, a sequential game is defined as a game where one player selects their action before others, and subsequent players are informed of that choice before making their own decisions. This turn-based structure, governed by a time axis, d ...

s. If a player forgets past information, their current decisions may contradict their earlier intentions. The concept plays a key role in the relationship between mixed and behavioral strategies. In games where players have perfect recall, these two types of strategies are essentially equivalent, meaning that any outcome that can be achieved with a mixed strategy can also be achieved with a behavioral strategy, and vice versa. This equivalence, notably formalized in

Kuhn's theorem In game theory Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game t ...

, simplifies the analysis of such games.. It is a core component of how game theorists analyze extensive-form games. The formal definition of perfect recall involves the concept of information sets in extensive-form games. It ensures that if a player reaches a certain information set, the player's past actions and information are consistent with all the nodes within that information set. Games with players possessing perfect recall are often easier to analyze than those where players do not. Conversely, a lack of perfect recall by a player can lead to situations where that player is unable to execute planned strategies, affecting game outcomes.

References

Game theory Mathematical economics Economics theorems {{gametheory-stub

Significance

See also

References